We could solve the renormalization group equation for \(\overset{(1)}{\kappa }(t_1)\)  down to energy scales of practical experiments and apply the solution to different observables.
However, above \(t=t_1\) , or below \(M_1\) , the one-loop renormalization group equation of \(\overset{(1)}{\kappa }(t)\)  from Eq.(REF ) can not change its rankSee section 3.3 of [1]} for a more detailed analysis on why this is the case.
Therefore, we focus on the rank of \(\overset{(1)}{\kappa }(t_1)\)  to study if the matrix rank of \(\overset{(1)}{m_{eff}}(t_1)\)  is equal to the matrix rank of the high energy \(m_{eff}(0)\) .
